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Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

R. Allen LaCour, Timothy C. Moore, and Sharon C. Glotzer
Phys. Rev. Lett. 128, 188001 – Published 2 May 2022
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Abstract

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote—and, in some cases, may be necessary for—the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

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  • Received 11 December 2021
  • Revised 27 March 2022
  • Accepted 31 March 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.188001

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Polymers & Soft Matter

Authors & Affiliations

R. Allen LaCour, Timothy C. Moore, and Sharon C. Glotzer*

  • Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 48109, USA Biointerfaces Institute, The University of Michigan, Ann Arbor, Michigan 48109, USA

  • *sglotzer@umich.edu

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Issue

Vol. 128, Iss. 18 — 6 May 2022

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Images

  • Figure 1
    Figure 1

    Thermodynamic phase diagram for the binary inverse power law model (IPL) at γ=0.55, n=50, and kT/ε=1. Five phases are present: fluid, FCCL, FCCS, AlB2, and NaZn13. Dashed lines indicate three-phase coexistence.

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  • Figure 2
    Figure 2

    Self-assembly of AlB2. The plot in (a) shows the evolution of the number of large particles identified as AlB2 for NPT simulations at the given pressure and stoichiometry. All simulations at NL:NS=1:2 (colored blue on the plot) overlap substantially because they never exceed NAlB2=16. The plot in (b) shows the decay of the intermediate scattering function for certain combinations of stoichiometry and pressure. The lines are fits to the data. The dotted black line indicates the duration of simulations in (a). Snapshots of the results are shown for stoichiometries and pressures of (c) NL:NS=1:2, P*=70, (d) NLNS=1:3, P*=70, and (e) NL:NS=1:5, P*=75.

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  • Figure 3
    Figure 3

    Crystal growth in seeded simulations. The plot in (a) shows the evolution of the number of large particles identified as AlB2 from seeded simulations for different xs, Pσ3/ε, and initial seed size (Nseed). The image in (b) is a snapshot of the end of the seeded simulation at NL:NS=1:2 and Pσ3/ε=55. Large and small particles belonging to the initial seed are colored dark grey and light grey, respectively; large particles classified as mixed FCC-AlB2 are colored dark green. The plot in (c) shows the number of particles classified as AlB2 (NAlB2) versus the ratio of the number classified as mixed FCC-AlB2 to NAlB2 (Nmix/NAlB2). The insets illustrate the mixed FCC-AlB2 and AlB2 environments. The plot in (d) shows the chemical potential driving force ΔμC,F for the FCCL and AlB2 as a function of pressure and stoichiometry, where ΔμC,F is defined by Eq. (1). Errors (calculated as described in S2 of the Supplemental Material) are smaller than the size of the points.

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  • Figure 4
    Figure 4

    Self-assembly of hard cuboctahedra and octahedra. The plots show the radial distribution functions (RDFs) averaged over the final few frames of self-assembly at stoichiometries of (a),(c) 1:1 and (b),(d) 1:2. Also shown are the RDFs for a perfect CsCl structure. We show the RDF for large particles (gLL) and for large and small particles (gLS); the RDF for small particles is dominated by fluidlike small particles. Snapshots of the results are shown for (e) 1:1 and (f) 1:2.

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